Question

1. Today, a bond has a coupon rate of 8.18 percent, par value of 1,000 dollars, YTM of 6 percent, and semi-annual coupons with the next coupon due in 6 months. One year ago, the bond’s price was 1,022.04 dollars and the bond had 19 years until maturity. What is the current yield of the bond today? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

2. One year ago, a bond had a coupon rate of 10.5 percent, par value of $1000, YTM of 7.96 percent, and semi-annual coupons. Today, the bond’s price is 916.6 and the bond has 6 years until maturity. What was the current yield of the bond one year ago? The next coupon is due in 6 months. Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

3. Six months ago, a bond had a coupon rate of 7.28 percent, par value of $1000, YTM of 9.4 percent, and semi-annual coupons. Today, the bond’s price is 936.52 and the bond has 7 years until maturity. What was the current yield of the bond six months ago? The next coupon is due in 6 months. Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

Answer to Question 1:

Par Value = $1,000

Annual Coupon Rate = 8.18%
Annual Coupon = 8.18% * $1,000
Annual Coupon = $81.80

Semiannual Coupon = Annual Coupon / 2
Semiannual Coupon = $81.80 / 2
Semiannual Coupon = $40.90

Annual YTM = 6.00%
Semiannual YTM = 3.00%

Time to Maturity = 18 years
Semiannual Period = 36

Current Price = $40.90 * PVIFA(3.00%, 36) + $1,000 * PVIF(3.00%, 36)
Current Price = $40.90 * (1 - (1/1.03)^36) / 0.03 + $1,000 * (1/1.03)^36
Current Price = $40.90 * 21.832252 + $1,000 * 0.345032
Current Price = $1,237.97

Current Yield = Annual Coupon / Current Price
Current Yield = $40.90 / $1,237.97
Current Yield = 0.0330